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Accelerator Development Department BROOKHAVEN NATIONAL LABORATORY Associated Universities, Inc.

Upton, New York 11973

RHIC TECHNICAL NOTE No. 38

Accelerating Uranium in RHIC - I1

Surviving the, AGS Vacuum ’

M. J. Rhoades-Brown BNL

and

H. Gould LBL

May 5, 1988

ADAU3IC-38

Section I - Introduction 1 In an earlier report, the problems of accelerating fully. stripped

uranium ions in the AGS was investigated. Making the reasonable assumption

that an adequate source of uranium ions will eventually be available at the Tandem, the earlier report showed that a modest intermediate Linac (- 10 M V )

would be sufficient for injecting fully stripped uranium ions into the AGS.

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In this repart we take a different strategy (suggested in discussions with A.G. Ruggiero-). Rather than accelerating fully stripped uranium ions in the AGS, we take advantage of proposed improvements in the AGS vacuum, and

investigate the survival rate of charge 90+ uranium ions in the AGS. In this

way, the intermediate Linac would not be necessary, and the present injection scheme (Arrangement A of reference 1) would be adequate to accelerate uranium ions.

The choice of accelerating charge 90c uranium has many origins. If we assume the charge state for uranium during acceleration in the Booster is 33+

(the same as Ig7Au), then the top kinetic energy after the Boos.ter is 229.8 MeV/A. At this energy, experimental measurements of Anholt et al. show that

fully 50% of the uranium ions will be in a charge 90’ state after passing

through foil SB (Arrangement A of reference 1). Only 1% will be fully

stripped at these energies.

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A straightforward calculation shows that for magnetic rigidities

the top kinetic energy of charge 90+ uranium is 10.6

This is almost identical to fully stripped 19’7Au ions (10.7 GeV/A),

4 available in the AGS,

GeV/A.

and hence clearly shows this kinetic energy can be accommodated in RHIC. 4

The critical question to be addressed in forthcoming sections is ”Can

charge 90+ uranium. ions suryive the AGS. vacuum?”

Section I1 - Acceleration Cycle for Uranium in AGS In figures 1-5 a proposed acceleration cycle for charge 90+ uranium is

shown. An acceleration time of 0.6 seconds was assumed, and the deduced rf

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16R x-- c -- a (Sin 4 s )

where p is the magnet radius, R the accelerator radius, E, the total energy,

l q 1 = [7-2-7&[, and V, 4s the required voltage and phase. The harmonic number h, was taken to be twelve in this case. 4

At the present time, the exact method by which bunches will be stacked

in RHIC is not finalized. For this reason, two complete acceleration cycles

will be used for depletion studies. The first one will assume buckets are

filled one at a time from the Booster (h=l), until all twelve in the AGS are full. Taking the worst possible case, this means with a 0.6 second

acceleration time the first bunch must survive 11.6 seconds in the AGS. For

the second case we simply assume one bucket at a time is transferred from the Booster and accelerated in the AGS.

Section 111 - Depletion Rate of Uranium Ions in AGS The depletion rate of heavy ions in the AGS is defined as

(3)

where B(t) is the velocity of the 90+ uranium ions, ni is the density of gas

ions in the AGS, and g is the interaction cross section for uranium on

individual gas species. ig

ni is given by, ni - kP, where k is Boltzmanns constant, P is the For air w e assume pressure in Torr and k - 3.22 x

75.5% T5N, 23.2% 160, and 1.3% 40Ar. molecules/cm3 Torr.

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voltage and phase fall well within acceptable limits. 4 These values were

deduced assuming a constant bucket area X of 0.3 eV sec/A/bunch 4 , and solving 6 the usual pair of equations;

~ p R & - - sin +s 27r

oig is the sum of the stripping cross section aig, k and the capture cross section a? For the stripping cross section we assume the theory of Bethe, 6

7 *

which has been tested for uranium by Gould et al. In this theory ak is

given by : ig

where a is the fine structure constant, a, the Bohr radius of Hydrogen, Zi the atomic 'number of the gas molecule and Bk the binding energy of the k-shell

electrons in uranium, in units of Rydbergs. fk is an oscillator constant that takes the value -58 for 90+ uranium. The kinetic factors /3,7 are given by the acceleration cycle.

Neglecting finite nuclear size effects and Q.E.D. the binding energy of 8 an electron in uranium is given by Diracs theory as:

E = 2 mc

( 5 ) 2 2

ZCY 1 +

(n'+

For uranium atoms: K Shell Degeneracy = 2 Binding Energy = 132.36 KeV IS It = 34.24 KeV L Shell = 8 11 1: 11 = 6.4 KeV M Shell = 18

The capture cross section (Radioactive Electron Capture) into the . n' th 7 shell is given by

where m is the mass of an electron and Bn is the binding energy in the nth shell. g ( ~ ) is the photoionization cross section, which is tabulated for

various shells in uranium. 9 E is the photon energy, given by

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In figures 6 and 7, the photoionization cross section a(.) is shown for

capture to all shells and capture to all shells minus the k-shell. It can be seen that the contribution from the k-shell is significant at these energies,

and hence accelerating 90+ uranium has definite advantages regarding capture ~

The photon energy in figures 6 and 7 were deduced from equation ( 7 ) , where y

is the Lorentz factor for the accelerating uranium atom.

Figures 8 and 9 show the knock-out and capture cross sections for + N as a function of both the uranium kinetic energy and the acceleration time. It can.be seen that stripping dominates over capture at these energies, and

indeed at energies greater than 3 GeV/A, capture processes can be safely

ignored. The stripping cross section increases as a logarithm of y (see

equation 4 ) . Of course, the decrease of the capture cross section at these

energies is precisely the reason why accelerating fully stripped ions in the AGS is preferred. For fully stripped ions the stripping cross sectcion does

not exist of course, and for energies greater than a few GeV/A, capture is negligible.

Figure 10 shows the quantity X(t) defined in equation ( 3 ) for 90c

uranium I 5 N as a function of the acceleration time. It can be seen that the shape of A(t> is dominated by the stripping cross section. The small

discontinuity in X(t) at - .2 sec represents the effect of neglecting capture

cross sections at energies in excess of 3 GeV/A. This effect is seen to be

negligible.

Section IV - Survival Ratio in the AGS Assuming uranium intensities that are normalized to unity at time t=O,

figures 11-15 show the total depletion as a function of time in the AGS for various pressures. Figures 11 and 14 correspond to the full cycle of 11 second plus . 6 seconds acceleration, whereas figure 15 corresponds to the . 6

second acceleration cycle only. The depletion D is defined by:

X (t' ) dt ' t D(t) - e-Jo

where X(t') is given in equation ( 3 ) .

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It is very encouraging to see that for a pressure of torr, up to

91% of.the beam can be expected to survive the full 11.6 second acceleration cycle. For the

present day pressure' of torr, the beam will be depleted by a factor - 2 . 5 .

For a pressure of lo" torr, 99% can be expected to survive.

If the bunch of uranium ions is transferred from the Booster one at a time and accelerated in the AGS singularly (Figure 15) , then at torr 95%

of the beam will survive. At torr 98% will survive the short

acceleration cycle.

All of these results are extremely encouraging and positive for they clearly show that accelerating uranium in the AGS is feasible, even with a

vacuum of torr. Indeed, if as expected a vacuum of torr can be

achieved, then the full 12 bucket cycle, injected from the Booster, may be easily accommodated.

Of .course, all this analysis assumes an adequate- source of uranium ions

is available at the Tandem.

Section V - Conclusions and Suegestions for the Future 1) The analysis presented in this paper shows very clearly that it is

possible to accelerate uranium ions in a 90' charge state in the AGS,

even under current vacuum specifications, and have sufficient numbers of

ions survive the acceleration cycle for experimental purposes. Indeed

if the AGS vacuum can reach torr, as is expected in the very near

future, then a full 12 bucket acceleration cycle will only result in a l o s s of 8% of the uranium ions. For less severe acceleration cycles,

the depletion of uranium ions will be less and may be readily extracted

from figures 10 and 15, because of the exponential nature of the

depletion rate.

2) The energy, after acceleration in the AGS, of charge 90+ uranium ions is 10.6 GeV/A. After acceleration in the AGS these ions would be passed

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through a stripping foil and the fully stripped uranium, ions could be easily accommodated in RHIC.

3) The smival rate of charge 90 uranium ions in the AGS at and

torr, strongly indicates that there is relatively little to be gained by going to lQ" torr pressure in the AGS.

4) Adding uranium ions to the available list of heavy ions would increase the interest of the experimental community at: both fixed target AGS

experiments and future RHIC experiments. The extra nuclear charge

available would open up the experimental study of strong field Quantum

Electrodynamics, and the possible exotic modes these fields can excite

in nuclei.

5) The recent, extremely encouraging results in ion source development

strongly suggests that funding be made available to develop negative ion

sources for uranium at the Tandem.

References

1) Accelerating Uranium in RHIC - I. The Problems and Role of an

Intermediate Linac. M . J . Rhoades-Brown, RHIC Technical Note 35.

2) P. Thieberger, private communication.

3) R. Anholt, et al. Phys. Rev. (1987) 1586.

4 ) Conceptual Design of the Relativistic Heavy Ion Collider, RHIC, BNL 51932, May 1986.

5) "Proton Synchrotron Accelerator Theory" E. Wilson, CERN 77-07.

6) H.E. Bethe, Ann. Phys. 5 (1930) 325, ' 7) H. Gould, et al. Phys. Rev. Lett. 2 (1984) 180.

Erratum Phys. Rev. Lett. 2 (1984) 1654. 8) "Advanced Quantum Mechanics" J . J . Sakurai (1967) page 1-27.

9) ' R.M. Pratt, et al. Reviews in Modern Physics, 45 (1973) 273.

-k Supported by Chemical Sciences Division under contract no. USDOE-DE-AC-

03-76SF00098 with Lawrence Berkeley Laboratory

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Figure Captions

Figure 1. Time variation of the dipole magnetic field for the 0.6 second acceleration cycle.. '.

Figure 2. Rate of charge of dipole magnetic field for acceleration cycle.

Figure 3 . Time variation of rf voltage during acceleration cycle to maintain bucket area of . 3 eV sec/A/bunch.

Figure 4 . Graph of rf phase during acceleration cycle, showing- Jump across transition energy at .44 seconds.

Figure.5. Kinetic energy of charge 90 uranium ion during acceleration cycle.

Figure 6 . Photoionization cross section for uranium, showing capture to all major shells.

Figure 7. As figure 5 , except: the k-shell capture has been removed.

Figure 8. The knock-out and capture cross sections for uranium ions as a

function of kinetic energy during the acceleration cycle. The

cross sections are for charge 90 uranium on nitrogen.

Figure 9. A s figure 8, but plotted against acceleration time.

Figures 10-14. Depletion of charge 90 uranium ions as function of AGS acceleration cycle. The depletion is shown for various AGS pressures.

Figure 15. Depletion of charge 90 uranium ions for short 0.6 second

acceleration cycle in AGS only.

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Figure 4 . Graph of rf phase during a c c e l e r a t i o n cycle , showing jump ac ross I

' IW, t r a n s i t i o n energy a t .44 seconds.

J a P

li:

lh

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l-i (d

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u

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s-

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Figure 8. The knock-out and capture cross sec t ions f o r uranium ions as a func t ion of k i n e t i c energy during t h e acce le ra t ion cycle . f o r charge 90 uranium on n i t rogen .

The c ross s e c t i o n s are

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